Checking the adequacy for a distortion errors-in-variables parametric regression model

Zhang, Jun; Li, Gaorong; Feng, Zhenghui

doi:10.1016/j.csda.2014.09.018

Cited by 29 publications

(10 citation statements)

References 33 publications

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“…Condition (C4) is the condition for the bandwidth h in the nonparametric kernel smoothing. Conditions (C5) and (C6) is used for the nonlinear least squares estimator (Cui et al, ; Wu, ; Zhang, Li, & Feng, ; Zhang, Lin, & Li, ).…”

Section: Estimation Methods and Asymptotic Resultsmentioning

confidence: 99%

Logarithmic calibration for multiplicative distortion measurement errors regression models

Zhang

Yang

2020

Statistica Neerlandica

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In this article, we propose a new identifiability condition by using the logarithmic calibration for the distortion measurement error models, where neither the response variable nor the covariates can be directly observed but are measured with multiplicative measurement errors. Under the logarithmic calibration, the direct-plug-in estimators of parameters and empirical likelihood based confidence intervals are proposed, and we studied the asymptotic properties of the proposed estimators. For the hypothesis testing of parameter, a restricted estimator under the null hypothesis and a test statistic are proposed. The asymptotic properties for the restricted estimator and test statistic are established. Simulation studies demonstrate the performance of the proposed procedure and a real example is analyzed to illustrate its practical usage.

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Section: Estimation Methods and Asymptotic Resultsmentioning

confidence: 99%

Logarithmic calibration for multiplicative distortion measurement errors regression models

Zhang

Yang

2020

Statistica Neerlandica

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“…, ψn (u) and γnr (u) being defined in the Appendix A. The calibrated method can also refer to Zhang et al (2015). Here, we apply the local linear method to estimate ψ(u) and γ(u).…”

Section: Estimation Of the Null Hypothesis Modelmentioning

confidence: 99%

“…where X ∼ U 2 [1, 2]. These models are also considered by Zhang et al (2015). Set (β 1 , β 2 ) = (2, 3), C = 0.0, 0.2, 0.4, 0.6, 0.8 and (β 1 , β 2 ) = (1, 2), C = 0.0, 0.1, 0.2, 0.3, 0.4 for models (5.9) and (5.10), respectively.…”

Section: Simulation Studies17mentioning

confidence: 99%

See 1 more Smart Citation

Efficient Diagnostics for Parametric Regression Models with Distortion Measurement Errors Incorporating Dimension-reduction

Sun¹,

Chen²,

Liang³

2022

STAT SINICA

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In this work, we study the diagnostics of parametric regression models when both the response variable and covariates are distorted with errors. We employ a projected empirical process to develop Cramér-von Mises and Kolmogorov-Smirnov tests with dimension-reduction effects. We apply random approximation to enable the expedient calculation of Kolmogorov-Smirnov test for checking the suitability of regression models. The proposed tests are shown to be consistent and can detect an alternative hypothesis close to the null hypothesis at the root−n rate. Simulation studies show that the proposed tests outperform the existing methods. A real data set is analyzed for illustration.

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“…Recently, Zhang, Gai and Wu () considered the estimation for linear and non‐linear models with multivariate confounding variables. Z HANG , L I and F ENG () proposed an empirical process test statistic based on residuals to solve the problem of model checking on parametric distortion measurement error regression models.…”

Section: Introductionmentioning

confidence: 99%

Statistical inference on restricted partial linear regression models with partial distortion measurement errors

Zhang

Zhou

Sun

et al. 2016

Statistica Neerlandica

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We consider the estimation and hypothesis testing problems for the partial linear regression models when some variables are distorted with errors by some unknown functions of commonly observable confounding variable. The proposed estimation procedure is designed to accommodate undistorted as well as distorted variables. To test a hypothesis on the parametric components, a restricted least squares estimator is proposed under the null hypothesis. Asymptotic properties for the estimators are established. A test statistic based on the difference between the residual sums of squares under the null and alternative hypotheses is proposed, and we also obtain the asymptotic properties of the test statistic. A wild bootstrap procedure is proposed to calculate critical values. Simulation studies are conducted to demonstrate the performance of the proposed procedure, and a real example is analyzed for an illustration.

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Checking the adequacy for a distortion errors-in-variables parametric regression model

Cited by 29 publications

References 33 publications

Logarithmic calibration for multiplicative distortion measurement errors regression models

Logarithmic calibration for multiplicative distortion measurement errors regression models

Efficient Diagnostics for Parametric Regression Models with Distortion Measurement Errors Incorporating Dimension-reduction

Statistical inference on restricted partial linear regression models with partial distortion measurement errors

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